In gambling, the chances of winning are often written in terms of odds rather th

Question

In gambling, the chances of winning are often written in terms of odds rather than probabilities. The odds of wining is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcome. For example, if the number of successful outcomes is 2 and the number of unsuccessful outcomes is 3, the odds of wining are 23("2to3") or 2/3, The odds of an event occurring are 3.5. Find (a) the probability that the event will occur and (b) the probability that the event will not occur. (a) The probability that the event will occur is (b) The probability that the event will not occur is

Explanation / Answer

a) Probability that event will occur:

Odds = 3:5

Probability that event will occur = 3/(3+5) = 3/8

b) Probability that event will not occur:

Odds of occuring = 3:5

Probability that event will occur = (5-3)/(3+5) = 2/8 = 1/4

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